This gets more interesting with each note. The time system used on the sundials in Istanbul, Topkapi Palace and various mosques, makes it easier to assign all the hour numbers. They assigned 6 to noon. On the equinox all the lines cross the meridian at 6. The others then fall into place. The horizontal 12 line on the south facing dial is interesting. On a horizontal dial, the lines continue as summer days have more than 12 equal hours. In Istanbul they used two 12 hour cycles so there were no numbers in the teens and twenties.
Roger Bailey Walking Shadow Designs -------------------------------------------------- From: "Frank King" <frank.k...@cl.cam.ac.uk> Sent: Friday, April 02, 2010 4:12 AM To: "Gianni Ferrari" <gfme...@gmail.com> Cc: "LISTA INGLESE" <sund...@rrz.uni-koeln.de> Subject: Re: how italian hours > Dear Gianni, > > Your analysis has silenced the Lista Inglese! > > I will summarise what you said so that new > readers may start here... > > You have: > > D = length of day (sunrise to sunset) > > Whenever D is an integer number of hours, the > associated constant-declination curve passes > through a hyperbolic arc of points at which > Babylonian and Italian hour-lines intersect. > > Whenever D is an EVEN integer number of hours, > the associated constant-declination curve passes > through a hyperbolic arc of points at which > Babylonian, Italian AND French hour-lines > intersect. > > Whenever D is 6, 12 or 18 hours, the associated > constant-declination curve passes through a > hyperbolic arc of points at which Babylonian, > Italian, French AND Temporary hour-lines > intersect. > > This makes 58.49 degrees North an interesting > latitude to set up a dial because: > > At the winter solstice D = 6 hours > At the equinoxes D = 12 hours > At the summer solstice D = 18 hours > > I attach a PDF which shows a dial marked out for > a direct south-facing wall at this latitude. > > The Babylonian, French and Italian hour-lines > are obvious and I have drawn the Temporary hours > in blue to distinguish them. > > Design exercise for the reader: > > Number all the lines in an elegant way! > > The equinoctial line has quadruple crossing points > all along it. > > The winter and summer solstice curves have these > quadruple crossing points at noon and at: > > B=6, F=9, I=12, T=4 and B=12, F=15, I=18, T=8 > > There are, of course, triple crossing points along > the D=6, 8, 10, 12, 14, 16 and 18 hyperbolae where > Babylonian, French and Italian hour-lines intersect. > > There are a few "surprise" triple crossing points > too such as those at: > > B=5 I=14, T=4 and B=10, I=19, T=8 > > The French hours at these points are half-integers. > > One more thing: > > Babylonian, French and Italian hour-lines are > STRAIGHT on a plane dial. Temporary hour-lines > are narrow S-shapes. Print out my attachment > and squint along the blue lines. You will see > that they are gentle curves. > > It is very cold here at 52 degrees north so I shall > not be moving to 58.49 degrees north myself :-) > > Best wishes > > Frank > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > > --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
